Readers can look at my previous replies on the thread on pi for some more on this topic, but here I will emphasize the "near-square primes" (see for example Wikipedia online or Wolfram/Eric Weisstein online articles on "Near-Square Primes" and similar articles). A considerable number of primes p are generated by equations of the form:

1) p = n^2 +/- m (or y^2 - x for x, y positive integers)

While (1) z = y^2 +/- x or n^2 +/- m for x, y positive integers does not guarantee by any means that z is a prime, a considerable number of primes are generated by this type of equation, with k = +/- 1, +/- 2, +/- 3, +/- 4, +/- 5. The case +/- 1 is especially interesting because with n^2 or y^2 replaced by slightly different functions, for example by 2^n, 2^k 3^j, n2^n, 2n or 2p, n!, we generate not only many primes but many important named primes like Mersenne Primes, Pierpoint Primes, Woodall primes, Sophie Germain primes, Twin Primes, Cousin Primes, Factorial Primes.